Integrated sensing and communication (ISAC) provides a spectrum-efficient approach for simultaneously enabling reliable data transmission and high-quality sensing. This article investigates an ISAC-enabled multidevice cooperative sensing system in which the devices perform cooperative sensing toward multiple targets in a time-division manner. Within the allocated time, each device senses the targets and transmits data to the base station simultaneously via ISAC. To investigate this problem, we formulate a joint optimization of the beamforming for both sensing and transmission as well as the time allocation for different devices, aiming at maximizing the total throughput of the devices while guaranteeing the multitarget sensing quality, the cooperative sensing requirement and the fairness in data transmission. To tackle the nonconvexity of the formulated problem, we first decompose the problem into a beamforming subproblem and a time allocation subproblem. Subsequently, we transform the beamforming subproblem into a tractable form. We then analyze the feature of the optimal time allocation in the time allocation subproblem while providing its semi-analytical expression, based on which we further propose an efficient algorithm to solve the original problem. Simulation results validate the effectiveness of our algorithm and the performance advantages of our fairness-aware ISAC-enabled cooperative sensing in improving both throughput and cooperative sensing accuracy.